An astronomer of Leipzic found it soon after; but, with the mean jealousy of a miser, he concealed his treasure, while his contemporaries throughout Europe were vainly directing their anxious search after it to other quarters of the heavens. At this time, Delisle, a French astronomer, and his assistant, Messier, who, from his unweared assiduity in the pursuit of comets, was called the Comet-Hunter, had been constantly engaged, for eighteen months, in watching for the return of Halley's comet. Messier passed his life in search of comets. It is related of him, that when he was in expectation of discovering a comet, his wife was taken ill and died. While attending on her, being withdrawn from his observatory, another astronomer anticipated him in the discovery. Messier was in despair. A friend, visiting him, began to offer some consolation for the recent affliction he had suffered. Messier, thinking only of the comet, exclaimed, "I had discovered twelve: alas, that I should be robbed of the thirteenth by Montague!"—and his eyes filled with tears. Then, remembering that it was necessary to mourn for his wife, whose remains were still in the house, he exclaimed, "Ah! this poor woman!" (ah! cette pauvre femme,) and again wept for his comet. We can easily imagine how eagerly such an enthusiast would watch for Halley's comet; and we could almost wish that it had been his good fortune to be the first to announce its arrival: but, being misled by a chart which directed his attention to the wrong part of the firmament, a whole month elapsed after its discovery by Palitzch, before he enjoyed the delightful spectacle.
The comet arrived at its perihelion on the thirteenth of March, only twenty-three days from the time assigned by Clairaut. It appeared very round, with a brilliant nucleus, well distinguished from the surrounding nebulosity. It had, however, no appearance of a tail. It became lost in the sun, as it approached its perihelion, and emerged again, on the other side of the sun, on the first of April. Its exhibiting an appearance, so inferior to what it presented on some of its previous returns, is partly accounted for by its being seen by the European astronomers under peculiarly disadvantageous circumstances, being almost always within the twilight, and in the most unfavorable situations. In the southern hemisphere, however, the circumstances for observing it were more favorable, and there it exhibited a tail varying from ten to forty-seven degrees in length.
In my next Letter I will give you some particulars respecting the late return of Halley's comet.
LETTER XXVI.
COMETS, CONTINUED.
"Incensed with indignation, Satan stood Unterrified, and like a comet burned, That fires the length of Ophiucus huge In the Arctic sky, and from his horrid train Shakes pestilence and war."—Milton.
Among other great results which have marked the history of Halley's comet, it has itself been a criterion of the existing state of the mathematical and astronomical sciences. We have just seen how far the knowledge of the great laws of physical astronomy, and of the higher mathematics, enabled the astronomers of 1682 and 1759, respectively, to deal with this wonderful body; and let us now see what higher advantages were possessed by the astronomers of 1835. During this last interval of seventy-six years, the science of mathematics, in its most profound and refined branches, has made prodigious advances, more especially in its application to the laws of the celestial motions, as exemplified in the 'Mecanique Celeste' of La Place. The methods of investigation have acquired greater simplicity, and have likewise become more general and comprehensive; and mechanical science, in the largest sense of that term, now embraces in its formularies the most complicated motions, and the most minute effects of the mutual influences of the various members of our system. You will probably find it difficult to comprehend, how such hidden facts can be disclosed by formularies, consisting of a's and b's, and x's and y's, and other algebraic symbols; nor will it be easy to give you a clear idea of this subject, without a more extensive acquaintance than you have formed with algebraic investigations; but you can easily understand that even an equation expressed in numbers may be so changed in its form, by adding, subtracting, multiplying and dividing, as to express some new truth at every transformation. Some idea of this may be formed by the simplest example. Take the following: 3+4=7. This equation expresses the fact, that three added to four is equal to seven. By multiplying all the terms by 2, we obtain a new equation, in which 6+8=14. This expresses a new truth; and by varying the form, by similar operations, an indefinite number of separate truths may be elicited from the simple fundamental expression. I will add another illustration, which involves a little more algebra, but not, I think, more than you can understand; or, if it does, you will please pass over it to the next paragraph. According to a rule of arithmetical progression, the sum of all the terms is equal to half the sum of the extremes multiplied into the number of terms. Calling the sum of the terms s, the first term a, the last h, and the number of terms n, and we have (½)n(a+h)=s; or n(a+h)=2s; or a+h=2s⁄n; or a=(2s⁄n)-h; or h=(2s⁄n)-a. These are only a few of the changes which may be made in the original expression, still preserving the equality between the quantities on the left hand and those on the right; yet each of these transformations expresses a new truth, indicating distinct and (as might be the case) before unknown relations between the several quantities of which the whole expression is composed. The last, for example, shows us that the last term in an arithmetical series is always equal to twice the sum of the whole series divided by the number of terms and diminished by the first term. In analytical formularies, as expressions of this kind are called, the value of a single unknown quantity is sometimes given in a very complicated expression, consisting of known quantities; but before we can ascertain their united value, we must reduce them, by actually performing all the additions, subtractions, multiplications, divisions, raising to powers, and extracting roots, which are denoted by the symbols. This makes the actual calculations derived from such formularies immensely laborious. We have already had an instance of this in the calculations made by Lalande and Madame Lepaute, from formularies furnished by Clairaut.
The analytical formularies, contained in such works as La Place's 'Mecanique Celeste,' exhibit to the eye of the mathematician a record of all the evolutions of the bodies of the solar system in ages past, and of all the changes they must undergo in ages to come. Such has been the result of the combination of transcendent mathematical genius and unexampled labor and perseverance, for the last century. The learned societies established in various centres of civilization have more especially directed their attention to the advancement of physical astronomy, and have stimulated the spirit of inquiry by a succession of prizes, offered for the solutions of problems arising out of the difficulties which were progressively developed by the advancement of astronomical knowledge. Among these questions, the determination of the return of comets, and the disturbances which they experience in their course, by the action of the planets near which they happen to pass, hold a prominent place. In 1826, the French Institute offered a prize for the determination of the exact time of the return of Halley's comet to its perihelion in 1835. M. Pontecoulant aspired to the honor. "After calculations," says he, "of which those alone who have engaged in such researches can estimate the extent and appreciate the fastidious monotony, I arrived at a result which satisfied all the conditions proposed by the Institute. I determined the perturbations of Halley's comet, by taking into account the simultaneous actions of Jupiter, Saturn, Uranus, and the Earth, and I then fixed its return to its perihelion for the seventh of November." Subsequently to this, however, M. Pontecoulant made some further researches, which led him to correct the former result; and he afterwards altered the time to November fourteenth. It actually came to its perihelion on the sixteenth, within two days of the time assigned.
Nothing can convince us more fully of the complete mastery which astronomers have at last acquired over these erratic bodies, than to read in the Edinburgh Review for April, 1835, the paragraph containing the final results of all the labors and anticipations of astronomers, matured as they were, in readiness for the approaching visitant, and then to compare the prediction with the event, as we saw it fulfilled a few months afterwards. The paragraph was as follows: "On the whole, it may be considered as tolerably certain, that the comet will become visible in every part of Europe about the latter end of August, or beginning of September, next. It will most probably be distinguishable by the naked eye, like a star of the first magnitude, but with a duller light than that of a planet, and surrounded with a pale nebulosity, which will slightly impair its splendor. On the night of the seventh of October, the comet will approach the well-known constellation of the Great Bear; and between that and the eleventh, it will pass directly through the seven conspicuous stars of that constellation, (the Dipper.) Towards the end of November, the comet will plunge among the rays of the sun, and disappear, and will not issue from them, on the other side, until the end of December."